Kentucky

This Kentucky flag design isn't exactly what I was looking for, but it's probably better than the current flag.
The shape of the flag resembles a capital letter "K", for Kentucky. The black and white represents Abraham Lincoln, who was born in the state. I made the negative space of the flag an equilateral triangle to also represent Lincoln (all sides are equal). The blue-green background represents bluegrass music, which is popular in Kentucky. The pennant shape of the flag makes it last longer when flying in the wind.

Look at the current Kentucky flag, and you'll see that it is horrible, like most of the U.S. state flags.

Illinois

This flag is kind of based off of the Chicago flag, which is great!

The blue stripe by the hoist represents the Mississippi River. The quarter-circle represents Lake Michigan. The six stars represent the six states which border Illinois; Wisconsin. Michigan, Indiana, Kentucky, Missouri, and Iowa. There are a total of 102 points on the six stars, which represent the 102 counties of Illinois. The "L" shape of the stars represents Abraham Lincoln, and the state's nickname, "The Land of Lincoln". Also, the blue stripe and the "L" resembles "IL", the state's abbreviaton.

The current Illinos flag is stupid. And the guy who designed it obviously didn't know what he was doing. (duh?) The government of Illinois added the word "ILLINOIS" to the flag so that people would recognize it. If the flag wasn't so complicated, they wouldn't need the words; people would recognize that.